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A penalty-based aggregation operator for non-convex intervals
journal contribution
posted on 2014-11-01, 00:00 authored by Gleb BeliakovGleb Beliakov, Simon JamesSimon JamesIn the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.
History
Journal
Knowledge-based systemsVolume
70Pagination
335 - 344Publisher
Elsevier BVLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0950-7051Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2014, ElsevierUsage metrics
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